Will NPCs poisoned weapons run out of poison

You can change the default autorun state from on to off by editing the game's preference file, which is located in:

My Documents/My games/Skyrim/SkyrimPrefs.ini

In there, you can find the section [Controls] which has a setting

bAlwaysRunByDefault=1

Change it to:

bAlwaysRunByDefault=0

To turn autorun off by default.

No. Spells, Magical enchantments, and Poison damage are never multiplied by sneak / power attack multipliers.

Weergh! indeed.

I've been shooting arrows at this Windhelm guard. As you can see in my screenshot, there's 4 listed health values:

316.00 - this is the guard's base health

268.35 - this is a shot from my normal bow. It includes a 15 damage fire enchant. This implies that my bow shot did 33 damage, and 15 fire damage.

204.53 - this is a sneak attack from my bow. I have the 3x sneak attack perk w/ bows. Our assumption is that magical enchantments do not get multiplied in. Indeed, subtracting the 15 fire damage, we get 97, which is about equal to 33 * 3 (the difference in 2 expected damage is probably because he's on fire; ideally, I'd have tested with frost or shock, but didn't have one of those on me)

189.55 - sneak attack with bow, as above, but this time I added a 15 damage poison to my bow. This means after you subtract 15 from the fire enchantment and 15 from the poison, we dealt 97 damage again. (so it looks like my first shot was probably around 32.33, instead of the 33 I rounded it to.)

Conclusion: magical enchantments and poisons do not get multiplied.